The motion of the tubes with their ends on the wire represents a certain amount of energy, commonly regarded as kinetic, and styled electrokinetic energy. If c denote the current, that is, the rate, -dQ⧸dt, at which the charge of the condenser is being changed, and L a quantity called self-inductance, depending mainly on the arrangement of the connecting wire--whether it is wound in a coil or helix, with or without an iron core, or not--the electrokinetic energy will be ½Lc². This is analogous to the kinetic energy ½mv² of a body (say a pendulum bob) of mass m and velocity v, so that L represents a quantity for the conducting arrangement analogous to inertia, and c is the analogue of the velocity of the body. The whole energy at any instant is thus ½Q²⧸C + ½Lc², or ½Q²⧸C + ½L(dQ⧸dt)². The loss of energy due to heating of the conducting connection is not completely understood, though its quantitative laws have been quite fully ascertained and expressed in terms of magnitudes that are capable of measurement. It was found by Joule to be proportional to the second power, or square, of the current, and to a quantity R depending on the conductor, and called its resistance. The generation of heat in the conductor seems to be due to some kind of frictional action of particles of the conductor set up by the penetration of the Faraday tubes into it. A conductor is unable to bear any tangential action exerted upon it by Faraday tubes, which, however, when they exist, begin and end at material particles, except when they are endless, as they may be in the radiation of energy. When the Faraday tubes are moving with any ordinary speed they are not at their ends perpendicular to the conducting surface from which they start or at which they terminate, but are there more or less inclined to the surface, and consequently there is tangential action which appears to displace the particles (not merely at the surface, unless the alternation is very rapid) relatively to one another and so cause frictional generation of heat. The time rate of generation of heat is thus Rc², or R(dQ⧸dt)², when the units in which R and c are expressed are such as to make this quantity a rate of doing work in the true dynamical sense. This is the rate at which the sum of energy already found is being diminished, and so the equation ½d/dt{(Q²⧸C) + L(dQ⧸dt)²} = －R(dQ⧸dt)² holds, or leaving out the common factor dQ⧸dt, the equation L(d²Q⧸dt²) + R(dQ⧸dt) + Q⧸C = 0 This last equation was established by Thomson, and is precisely that which would be obtained for a pendulum bob of mass L, pulled back towards the position of equilibrium with a force Q⧸C, where Q is the displacement from the middle position, and having its motion damped out by resisting force of amount R per unit of the velocity.